Advanced Thermodynamics

Note 3Heat Effects

Lecturer: 郭修伯

Heat

• The manufacture of ethylene glycol:– The catalytic oxidation reaction is most effective when

carried out at temperatures near 250°C.

– The reactants, ethylene and air are heated to this temperature before they enter the reactor.

– Heat is removed from the reactor to maintain the reaction temperature at 250 °C and to minimize the production of CO2.

• Heat effects are important.

Sensible heat effects

• Heat transfer to a system in which there are no phase transition, no chemical reactions, and no changes in composition cause the temperature of the system to change.

• Relation:– Quantity of heat transferred– The resulting temperature change

• Two intensive properties establishes its state: U = U (T,V)

dVV

UdT

T

UdU

TV

),( VTUU

dVV

UdTCdU

TV

constant-volume

dTCdU V

mechanically reversible constant-volume process

2

1

T

T VdTCUQ

.OR.

dPP

HdT

T

HdH

TP

),( PTHH

dPP

HdTCdH

TP

constant-pressure

dTCdH P

mechanically reversible constant-pressure process

2

1

T

T PdTCHQ

• Since or , we need C = f (T).

• From empirical equation:

• For gases, it is the ideal-gas heat capacity, rather than the actual heat capacity, that is used in the evaluation of such thermodynamic properties as the enthalpy.– Calculate values for a ideal-gas state wherein ideal-gas heat capacities are used– Correction to real-gas value

• Ideal-gas heat capacities:

• The two ideal-gas heat capacities:

• The molar heat capacity of the mixture in the ideal-gas state:

2

1

T

T VdTCQ 2

1

T

T PdTCQ

22 DTCTBTAR

CP

22 DTCTBTAR

C igP

1R

C

R

C igP

igV

igPCC

igPBB

igPAA

igP CyCyCyCmixture

• With

)( 00

TTCdTR

CRH

HP

T

T

P

020

2200 )1(

3)1(

20

TTT

DT

CT

BAdT

R

CT

T

P

0T

T

Mean heat capacity; subscript “H” denotes a mean value specific to enthalpy calculations.

0TC

HT

HP

It can be used to evaluate HPC

),,,;,0(0

DCBATTICPHdTR

CT

T

P

The function name is ICPH

),,,;,0( DCBATTMCPHR

CHP

The function name is MCPH

Calculate the heat required to raise the temperature of 1 mol of methane from 260 to 600°C in a steady-flow process at a pressure sufficiently low that methane may be considered an ideal gas.

6377.115.273260

15.273600

0

T

T

J

EEMCPH

EEICPH

TTT

dTR

CdT

R

CRHQ

igP

T

T

P

19778

15.53315.873)0.0,6164.2,3081.9,702.1;15.873,15.533(314.8

)0.0,6164.2,3081.9,702.1;15.873,15.533(314.8

)1(3

10164.2)1(

2

10081.9)1(702.1314.8 33

0

622

0

3

0

15.873

15.5330

What is the final temperature when heat in the amount of 0.4 x 106 Btu is added to 25 (lb mol) of ammonia initially at 500 °F in a steady-flow process at 1 (atm)?

KFT 15.5335000

)5186.0,0.0,3020.3,578.3;,15.533( EETMCPHR

CHP

0TC

HT

HP

mol

J

mollb

Btu

n

QH 3721816000

25

104.0 6

Start with a value T T≧ 0, T converges no the final value T = 1250K

Latent heats of pure substances

• A pure substance is liquefied from the solid state of vaporized from the liquid at constant pressure, no change in temperature– The latent heat of fusion

– the latent heat of vaporization

• the coexistance of two phases– According to the phase rule, its intensive state is determined by jus

t one intensive property.

dT

dPVTH

sat

Latent heat Vapor pressure

• Rough estimates of latent heats of vaporization for pure liquids at their normal points (Trouton‘s rule):

• Riedel (1954):

– Accurate! Error rarely exceed 5%

– Water:

• latent heat of vaporization of a pure liquid at any temperature, (Watson, 1943):

10~n

n

RT

H

Absolute temperature of the normal boiling point

nr

C

n

n

T

P

RT

H

930.0

)013.1(ln092.1

Reduced temperature at Tn

Critical temperature (bar)

56.13577.0930.0

)013.155.220(ln092.1

n

n

RT

H 15.373314.856.13 nH

38.0

1

2

1

2

1

1

r

r

T

T

H

H

Given that the latent heat of vaporization of water at 100°C is 2257 J/g, estimate the latent heat at 300 °C.

38.0

1

2

1

2

1

1

r

r

T

T

H

H

886.01.647/15.573

577.01.647/15.373

?)300(

2257)100(

2

1

2

1

r

r

T

T

CH

CH

g

JCH 1371)300(2

Standard heat of reaction

• A standard state is a particular state of species at temperature T and at specified conditions of pressure, composition, and physical condition as e.g., gas, liquid, or solid.– Gases: the pure substance in the ideal-gas state at 1 bar.

– Liquids and solids: the real pure liquid or solid at 1 bar.

– All conditions for a standard state are fixed except temperature. Standard-state properties are therefore functions of temperature only.

• Heat of reaction:

igPP CC

PC

JHNHHN 461002

3

2

1298322

JHNHHN 9222023 298322

Standard heat of formation

• A formation reaction is defined as a reaction which forms a single compound from its constituent elements, e.g.,:

• The heat of formation is based on 1 mol of the compound formed.

• The standard heat of formation : 298.15 K

• The standard heat at 25°C for the reaction:

298fH

OHCHHOC 322 22

1

114408224 298)(2)(2)(2)( HClOHOHCl gggg

)92307)(4(224 298)(2)(2)( HClHHCl ggg

)241818)(2(22 298)(2)(2)(2 HOHOH ggg

Standard heat of combustion

• A combustion reaction is defined as a reaction between an element or compound and oxygen to form specific combustion products. – Many standard heats of formation com from standard

heats of combustion, measured calorimetrically.

– Data are based on 1 mol of the substance burned.

12579054 298)(104)(2)( HHCHC ggs

)393509)(4(444 298)(2)(2)( HCOOC ggs

)285830)(5(52

125 298)(2)(2)(2 HOHOH lgg

28773962

1654 298)(2)(104)(2)(2 HOHCOHCO gglg

Temperature dependence of ΔH°

• A general chemical reaction:

– standard heat of reaction:

– if the standard-state enthalpies of all elements are arbitrary set equal to zero as the basis of calculation:

– For standard reactions, products and reactants are always at the standard-state pressure of 1 bar:

...... 44332211 AvAvAvAv

i

iiHvH

i

fiii

ii HvHvH

dTCdH Pii

dTCdH Pii dTCvdHv Pi

iii

ii

dTCvHvdHvd Pii

ii

iii

ii )()(

Pi

iiP CvC

iiiHvH )(

dTCHd P

T

T

P dTR

CRHH

00

)( 00 TTCHH

HP

),,,;,( 00 DDDCDBDATTIDCPHRHH

)(),,,;,( 000 TTDDDCDBDATTMDCPHRHH

Calculate the standard heat of the methanol-synthesis reaction at 800 °C.

)(3)(2)( 2 ggg OHCHHCO

103566

)15.29815.1073()5.1615(314.890135

))(5135.0,6450.3,3815.10,663.7;15.1073,15.298(( 00

TTEEEMDCPHRHH

T

T

P dTR

CRHH

00

90135)110525(2006602980 KHH

What is the maximum temperature that can be reached by the combustion of methane with 20% excess air? Both the methane and the air enter the burner at 25°C.

)(2)(2)(2)(4 22 gggg OHCOOCH

802625)74520()241818)(2(3935092980 KHH

Maximum attainable temperature → adiabatic, Q = 0 → ΔH = 0

Reactants at 1 bar and 25°C1 mol CH4

2.4 mol O2

9.03 mol N2

Products at 1 bar and T K1 mol CO2

2 mol H2O0.4 mol O2

9.03 mol N2ΔH = 0

KH 298

15.298

15.298

TC

TCn

H

HP

iHPii

P

0298 HHH P

HPC

HT

29815.298

Start with T > 298.15 K and converge on a final value of T = 2066K

Catalytic reforming of CH4: )(2)()(2)(4 3 gggg HCOOHCH

Reactants at 1 bar and 600K1 mol CH4

2 mol H2O

Products at 1 bar and 1300 K0.87 mol CO3.13 mol H2

0.13 mol CO2

0.87 mol H2O

ΔH = 0

KH 298

15.298

15.298

TC

TCn

H

HP

iHPii

P

The only other reaction occurs: )(2)(2)(2)( gggg HCOOHCO

RH

2058133 298)(2)()(2)(4 HHCOOHCH gggg

41166298)(2)(2)(2)( HHCOOHCO gggg

Calculate the heat requirement.

16464742 298)(2)(2)(2)(4 HHCOOHCH gggg

Not independent, choose (1) and (3) reactions

PR HHHH 298

2058133 298)(2)()(2)(4 HHCOOHCH gggg

16464742 298)(2)(2)(2)(4 HHCOOHCH gggg

0.87 mol CH4 by (1) and 0.13 mol CH4 by (3)

200460)164647)(13.0()205813)(87.0(298 KH

34390

60015.298)5121.0,0.0,3450.1,470.3;15.298,600()(2(

)0.0,6164.2,3081.9,702.1;15.298,600()(1(314.8

60015.298

EEMCPH

EEMCPH

Cn

H

iHPii

R

16194015.2981300

i

HPii

P

Cn

H

328010298 PR HHHH

Steady flow, no shaft work, kinetic and potential energy changes are negligible

328010 HQ